Table of Contents
Exploring Geography Cartographically
Subjects To Be Covered
To begin I stress
There are many ways of specifying location
Other Ways of Determining Locations
Common Geographic Locational Aliases and Conversions
Hand Held GPS with MapLocations are estimated from distances
Wrist Watch GPS
The fact that locations can be determined by specifying distances can lead to some interesting results.
In the lower school grades one learns the procedure for finding distance from coordinates.
An Exercise Using Distances
A Similar, But Simpler, Exercise
Step by Step Trilateration
Trilateration Procedure Illustrated Graphically
The Beginning Steps
The Answer, with Coordinates and Estimated Distances
Solution to the US Distance Exercisewith (enlarged) estimated standard errors
Locations increase linearly, distances quadraticaly thusNo Numbers are Needed!
I will now give you another example where locations are estimated from distances
Cappadocian Cuneiform Tablet
Given the occurrence of town names on tablets
Use the well known gravity model:
Predicted Locationsof 33 Pre-Hittite Towns in Cappadocia using distances estimated from presumed interaction.
USA Highway Distance Map
This “distorted” map can be evaluated by the methods of Tissot
All maps are of course distorted to some extent
The Surface of the Earth Is Two-dimensional
The Map Projection Problem is to reduce the curved, closed, and bumpy two dimensional surface of the earth to a flat two dimensional surface
The Transform - Solve - Invert Paradigm
The conventional satellite tracking chart
Breckman Chart to Track Satellites
US Population By One Degree Quadrilaterals
The Lat/Lon Grid in the Two SpacesLeft, the usual grid. Right, transformed according to population.
US Map in the Two SpacesLeft, the usual map. Right, the transform.
The InversionOn the right are uniform hexagons in the transformed space. On the left is the solution: The inverse transformation partitions the US into cells of equal population
Most of you are familiar with linear regression and correlation
Title page from Ptolemy’s Geography
A Page from Ptolemy’s Geography
Ptolemy’s World Map
Ptolemy’s Map of Gaul(Modern France)
Modern and Ptolomaic Latitude and Longitude for Gaul
The data in the foregoing table were assembled by a student and some of you may be more familiar with the the ancient names than I.
Modern Latitude versus Ptolemy’s Latitude
Modern Longitude versus Ptolemy’s Longitude
Ptolemaic DisplacementsAmounts needed to move Ptolemy’s locations to modern locations. The places needing further investigation can be seen.
Interpolated Vector Field Amount needed to move the graticule to modern locations
Ptolemaic Grid Shifted to Fit Modern‘Pushed’ by the interpolated vector field
There are many applications of vectors (pairs of coordinates) in geography
But often we have observations assembled by statistical unitsCensus tracts, school districts, and the like
Population Density by County
Population Density in KansasBy CountyCourtesy of T. Slocum
Population Density in Kansasby CountyEach county still contains the same number of people
How Pycnophylactic Reallocation Works
Mass Preserving Reallocation Using Areal Data
What the Mathematics Means
Colored Clay Before Smoothing
Colored Clay After Smoothing
Another Advantage of Mass-Preserving Reallocation
The next important topic is
The Table is an Important Form of Geographic Movement Data
Let T represent the table, with i rows and j columns. It can be decomposed into two parts as follows: Tij = T+ + T–whereT+ = (Tij + Tji)/2 (symmetric)T– = (Tij - Tji)/2 (skew symmetric)
Both Parts Can Be Used
From B to A is Not the Same as A to B(Gary Larson)
Asymmetries Are a Fact of Geography
Table of Mail Delivery TimesObserve the asymmetry
A Map of Wind Computed from Mail Delivery Times
From Wind to Pressure Field
In the United States the Currency Indicates Where It Was Issued
Dollar Bill(Federal Reserve Note)
The 12 Federal Reserve Districts(Alaska and Hawaii omitted)
Movement of One Dollar Notes between Federal Reserve Districts, in hundreds, Feb. 1976 To: B NY P Cl R A Ch SL M K D SF
The Table of Dollar Bill Movements
Dollar Bill Movement in the U.S.
The Map is Computed Using a Continuous Version of the Gravity Model
First the Federal Reserve Districts Are “Rasterized”
Solving the Equations Yields the PotentialShown here by contours
Population movement in the United States
Nine Region Migration TableUS Census 1973(Note asymmetry)
The Population Change Information Can Be Positioned Locationally using centroids
Population Change at State Centroids
Gaining and Losing StatesBased on the marginals of a 48 by 48 migration table
The Conventional Net Movement MapBased on movement between state centroids(Computer sketch. Optimum deletion: values below mean ignored)
Using a model, this information can be converted to a potential field and its gradient
The Migration Potentials and Gradients
Migration Potentials and Streaklines
Recall that tens of millions of people are moving in the five year interval
That these migration maps resemble maps of wind or ocean currents is not surprising given that we in fact speak of migration flows and backwaters, and use many such hydrodynamic terms when discussing movement phenomena.
By the insertion of arbitrary areal boundaries, and by measuring the amount of flux across these boundaries, one can obtain information not contained in the original data, i.e., make a prediction.
Major Flux Across State Boundaries Predicted from the model and table marginals
The Previous Maps Have Used Observations based on StatesPatterns within urban areas could not be seen.
If we used the 3,141 counties of the United States the migration table could contain 9,862,740 numbers
The 9x106 numbers in a county to county table could not be comprehended without some vizualization techniques or without a model.
36,000 Communes of France
For a world table of international migration, refugee movements, commodity trade, one would have a table of nearly 40,000 entries.
Migration in SwitzerlandAt several levels of resolution(Guido Dorigo, University of Zürich)
Net Migration In SwitzerlandBy 3090 Gemeinde, 3.5 km resolution
Swiss Migration at Reduced ResolutionTo emphasize the filtering effect of resolution
In this presentation I have emphasized Location and Movement
I appreciate your attention and thank you.